Finite Group Databasebeta

← #14646764

Subgroups — #14646764

Order 2816.

388 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077327C211yesmaximal, characteristic
2#13067377C212yesmaximal, complemented
3#13067250C212yesmaximal
4#13066527C211yesmaximal, characteristic, complemented
5C11×#1307C211yesmaximal, characteristic, complemented
6C2×#66960C412yes—
7#10623008C2211yescharacteristic
8C11×#432C2212yes—
9C11×#423C2211yescharacteristic
10#10622742C412yes—
11#10622539C2212yes—
12C2×C4×C11⋊C8C2211yescharacteristic
13#10622451—22no—
14#10622447—22no—
15#10622118—22no—
16#10622117—22no—
17#10622102—24no—
18C2×#4339C2×C412yes—
19C2×C11×M16C2×C412yes—
20C2×C42×C11C2311yescharacteristic
21#66983—22no—
22C22×C11⋊C8C2×C411yescharacteristic
23C22×C11⋊C8C2×C411yescharacteristic
24#66960—44no—
25C2×#4313—22no—
26C2×C8×D11—22no—
27#66928D412yes—
28#66927Q811yescharacteristic
29C4×D44—22no—
30#66922Q811yescharacteristic
31C11×C4⋊C8—22no—
32C11×C4⋊C8—22no—
33C11×C22⋊C8—22no—
34C11×#97—22no—
35C22⋊(C11⋊C8)—22no—
36(C2×D11)⋊C8—24no—
37C4⋊(C11⋊C8)—22no—
38#66867—22no—
39C4×C11⋊C8D412yes—
40C4×C11⋊C8D412yes—
41#8630—111nomaximal, Sylow
42C22×C4×C11C22×C411yescharacteristic
43C22×C4×C11#4112yes—
44C2×C22⋊D11—22no—
45#4339—42no—
46#4339—42no—
47C2×D44—22no—
48C2×D44C4⋊C412yes—
49C2×C4×D11—22no—
50C2×Dic22C4⋊C412yes—
51C11×M16—42no—
52C2×C8×C11—22no—
53C2×C8×C11—42no—
54C42×C11C2×D412yes—
55C42×C11C2×D411yescharacteristic
56C42×C11C2×Q811yescharacteristic
57(C2×D11)⋊C4—24no—
58C4⋊Dic11—22no—
59C2×C11⋊C8—22no—
60C2×C11⋊C8—41no—
61C2×C11⋊C8—42no—
62C2×C11⋊C8C22⋊C412yes—
63C2×C11⋊C8C22⋊C411yescharacteristic
64C2×C11⋊C8C22⋊C411yescharacteristic
65#4313—44no—
66C8×D11—44no—
67#2931—111no—
68#1568—112no—
69#1536—112no—
70#1307—111no—
71#1307D1111yescharacteristic, complemented
72C23×C11#11711yescharacteristic
73C22×D11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—42no—
77C2×C4×C11C2×C22⋊C411yescharacteristic
78C2×C4×C11C2×C4⋊C411yescharacteristic
79C2×C4×C11#12112yes—
80C2×C4×C11C22⋊Q812yes—
81C22⋊D11—44no—
82C2×Dic11—22no—
83D44—42no—
84D44—44no—
85C4×D11—42no—
86C4×D11—42no—
87Dic22—42no—
88C8×C11—42no—
89C8×C11—82no—
90C11⋊C8—21no—
91C11⋊C8—22no—
92C11⋊C8—82no—
93C11⋊C8#10012yes—
94C2×#131—112no—
95#532—111no—
96#436—222no—
97C8×D4—222no—
98#432—112no—
99#432C2×D1112yes—
100#423C2×D1111yescharacteristic
101#408—112no—
102C2×C4×C8—111no—
103#335—222no—
104#334—222no—
105#329—224no—
106C22×C11—21no—
107C22×C11—22no—
108C22×C11#38011yescharacteristic
109C2×D11—42no—
110C2×D11—44no—
111C4×C11—21no—
112C4×C11—22no—
113C4×C11—22no—
114C4×C11C2×#10011yescharacteristic
115C4×C11#41311yescharacteristic
116Dic11—42no—
117C2×#41—112no—
118#131—444no—
119C2×M16—222no—
120C2×M16C4×D1112yes—
121C22×C8—111no—
122C22×C8—111no—
123C22×C8—222no—
124C4⋊Q8—111no—
125#127—111no—
126#124—112no—
127#121—222no—
128C4×D4—222no—
129C2×C42C22×D1111yescharacteristic
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8—222no—
133C22⋊C8—22no—
134C22⋊C8—224no—
135C22⋊C8—222no—
136#97—22no—
137#97—222no—
138C4×C8—112no—
139C4×C8—112no—
140C2×C11—41no—
141C2×C11#180011yescharacteristic
142C2×C11#181412yes—
143D11—82no—
144#41—442no—
145#41—442no—
146C2×Q8—112no—
147C2×D4—112no—
148C2×D4—222no—
149C2×D4—222no—
150C22×C4—222no—
151C22×C4C2×C4×D1111yescharacteristic
152C22×C4#433912yes—
153M16—42no—
154M16—444no—
155C2×C8—22no—
156C2×C8—42no—
157C2×C8—111no—
158C2×C8—112no—
159C2×C8—111no—
160C2×C8—222no—
161C2×C8—444no—
162C2×C8—441no—
163C2×C8—442no—
164C4⋊C4—222no—
165C22⋊C4—224no—
166C42D4×D1112yes—
167C42D4×D1111yescharacteristic
168C42Q8×D1111yescharacteristic
169C11#863011yescharacteristic, complemented, Sylow
170C23—222no—
171C23#6692511yescharacteristic
172Q8—442no—
173D4—442no—
174D4—444no—
175D4—444no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—222no—
180C2×C4—442no—
181C2×C4—442no—
182C2×C4C22⋊C4×D1111yescharacteristic
183C2×C4#6693712yes—
184C2×C4C4⋊C4×D1111yescharacteristic
185C2×C4#6694912yes—
186C8—42no—
187C8—82no—
188C8—112no—
189C8—221no—
190C8—222no—
191C8—882no—
192C22—21no—
193C22—22no—
194C22—442no—
195C22—444no—
196C22#1062228011yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—442no—
201C4D11×#10011yescharacteristic
202C4#1062236411yescharacteristic
203C2—41no—
204C2—882no—
205C2#1306860711yescharacteristic
206C2#1306866912yes—
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1307C2
socleC22×C11#380
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1307D11
hypocenterC11#8630
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13067377C2semidirect
4. #13066527C2semidirect
5. C11×#1307C2semidirect
71. #1307D11semidirect
169. C11#8630semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130773272
#130673772
#130672502
#130665272
C11×#13072
#863011